---
license: cc-by-sa-4.0
configs:
- config_name: default
  data_files:
  - split: image_level
    path: '*.parquet'
tags:
- uncertainty,
- calibration,
- soft-labels
- ambiguous
pretty_name: soft-digits
size_categories:
- 1K<n<10K
---

## Soft-digits Dataset

### Motivation
The dataset was developed to provide a controlled testbed for investigating the dynamics between human perceptual uncertainty and model-based uncertainty. By including human-level uncertainty for each class, the dataset enables a more detailed analysis of how machine learning models align with or diverge from human judgment in ambiguous scenarios.


### Composition
Each instance in the dataset consists of a grayscale image of a handwritten digit (0–9) with a resolution of 28x28 pixels. There are 7,190 instances in the dataset. The dataset is a curated sample constructed from a combination of two existing public datasets. The selection process was designed to capture samples across all difficulties; a detailed description of the sampling methodology can be found in the main text of the accompanying paper.  

#### Dataset Field Descriptions

*   **images** (list of size `[1, 28, 28]`): List representing the grayscale image.
*   **original_labels** (list): The original label associated with the source data.
*   **indices** (int64): The indices for each data instance.
*   **file_name** (string): The specific file name (e.g., `1.png`).
*   **human_uncert_mean** (double): The "mean uncertainty" ($u_{mean}$): the average magnitude of doubt across all annotators for an image.
*   **pct_ann_unsure** (double): The "unsure proportion" ($u_{prop}$): the fraction of annotators who expressed uncertainty at least once for a given image, capturing the consensus of doubt.
*   **soft_label_yes_unc_equal** (list of floats): Equally-weighted soft-labels ($soft_e$). Both "Yes" and "Unsure" selections receive a weight of 1 to form each annotator’s individual probability distribution. These individual distributions are then averaged to create the final image-level soft-label.   
*   **soft_label** (list of floats): Uncertainty-weighted soft-labels ($soft_w$). "Unsure" selections are down-weighted to 0.5 at the annotator level to reflect a lower class-likelihood, while "Yes" remains 1, before averaging the distributions.
*   **soft_label_argmax** (list of floats): New majority voted labels ($maj_n$). A one-hot encoded label representing the class that received the highest consensus from the human annotators, derived directly from the soft-label distributions.
*   **split** (string): The dataset split, either "train", "val", or "test".
*   **source** (string): The origin source, either "mnist" or "mukhoti".



### Collection Process
We explored four openly available digit datasets to identify samples that represent a broad spectrum of classification difficulty. We explored the standard MNIST, the Swedish historical handwritten dataset ARDIS, and two synthetic variants of Ambiguous-MNIST.
We first de-duplicated the datasets to ensure evaluation integrity. Following de-duplication, we performed cartography mapping using a simple one-hidden-layer feed-forward network. Guided by these steps, we selected MNIST and Mukhoti's distributional Ambiguous-MNIST as our primary sources. MNIST was chosen over ARDIS because its larger scale (70k vs 7,474 images) provides a richer tail of naturally occurring hard and ambiguous cases. Between the synthetic datasets, Mukhoti offered a more comprehensive distribution across the difficulty spectrum and better adheres to the natural data manifold compared to Weiss's variant. The resulting datasets were partitioned into training, validation, and test sets using stratified sampling to ensure the difficulty distribution remains consistent across splits. We enforced a constraint of at least 150 'easy' instances per digit in the training set to maintain sufficient class representation.


### Cleaning/Labeling
No extensive pre-processing or cleaning was performed on the human annotations. This was an intentional design choice to preserve the natural variance in annotations, thereby the release of the dataset allows for further research into separating informative human label variation from noise. Regarding data integrity, we have retained the vast majority of collected annotations to maintain a representative distribution. We only excluded a small subset of samples from a single annotator who reported a hardware display failure during their session.


### Licensing

The soft-digits dataset is released under the CC-BY-SA 4.0 license. This dataset is a combination of a

- re-annotated subset of the [MNIST](http://yann.lecun.com/exdb/mnist/) dataset, originally created by Yann LeCun and Corinna Cortes. (released under CC-BY-SA 3.0)
- re-annotated subset of the [distributional Ambiguous-MNIST](https://github.com/omegafragger/DDU) dataset, originally created by Jishnu Mukhoti, Andreas Kirsch, Joost van Amersfoort, Philip H.S. Torr, and Yarin Gal. (released under MIT license)